On Revision of Partially Specified Convex Probabilistic Belief Bases

We propose a method for an agent to revise its incomplete
probabilistic beliefs when a new piece of propositional information
is observed. In this work, an agent’s beliefs are represented by a set
of probabilistic formulae – a belief base. The method involves determining
a representative set of ‘boundary’ probability distributions
consistent with the current belief base, revising each of these probability
distributions and then translating the revised information into a
new belief base. We use a version of Lewis Imaging as the revision
operation. The correctness of the approach is proved. An analysis of
the approach is done against six rationality postulates. The expressivity
of the belief bases under consideration are rather restricted, but
has some applications. We also discuss methods of belief base revision
employing the notion of optimum entropy, and point out some of
the benefits and difficulties in those methods. Both the boundary distribution
method and the optimum entropy methods are reasonable,
yet yield different results.